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A spherical wineglass, known diameter, is brim full of wine. What is the width of any vertical parallel slice with a volume of 1/4 of the wine?

Assume that the height of the wineglass is known.

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"Spherical wineglass".. how is it meant? can we assume it is a full sphere, or chopped? –  Berci Oct 6 '12 at 8:44
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Spherical wineglasses would be rather frustrating, methinks ... –  Peter Smith Oct 6 '12 at 9:13
    
The wineglass is chopped –  D Abbott Oct 6 '12 at 9:16
    
The problem requires a formula where one cut face would be defined, it can be in the centre or elsewhere. –  D Abbott Oct 6 '12 at 10:23
    
Perhaps you mean a hemispherical wineglass? –  TonyK Oct 6 '12 at 10:43
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1 Answer

Use the disk (washer) method for the function $f(x):=\sqrt{R^2-x^2}$ on the interval $[x_0,x_0+h]\subset[-R,R]$ to get an equation satisfied by $x_0$ and $h$.

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